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Simplifying 2n2 + 8n + -336 = 0 Reorder the terms: -336 + 8n + 2n2 = 0 Solving -336 + 8n + 2n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '2'. 2(-168 + 4n + n2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-168 + 4n + n2)' equal to zero and attempt to solve: Simplifying -168 + 4n + n2 = 0 Solving -168 + 4n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '168' to each side of the equation. -168 + 4n + 168 + n2 = 0 + 168 Reorder the terms: -168 + 168 + 4n + n2 = 0 + 168 Combine like terms: -168 + 168 = 0 0 + 4n + n2 = 0 + 168 4n + n2 = 0 + 168 Combine like terms: 0 + 168 = 168 4n + n2 = 168 The n term is 4n. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4n + 4 + n2 = 168 + 4 Reorder the terms: 4 + 4n + n2 = 168 + 4 Combine like terms: 168 + 4 = 172 4 + 4n + n2 = 172 Factor a perfect square on the left side: (n + 2)(n + 2) = 172 Calculate the square root of the right side: 13.114877049 Break this problem into two subproblems by setting (n + 2) equal to 13.114877049 and -13.114877049.Subproblem 1
n + 2 = 13.114877049 Simplifying n + 2 = 13.114877049 Reorder the terms: 2 + n = 13.114877049 Solving 2 + n = 13.114877049 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + n = 13.114877049 + -2 Combine like terms: 2 + -2 = 0 0 + n = 13.114877049 + -2 n = 13.114877049 + -2 Combine like terms: 13.114877049 + -2 = 11.114877049 n = 11.114877049 Simplifying n = 11.114877049Subproblem 2
n + 2 = -13.114877049 Simplifying n + 2 = -13.114877049 Reorder the terms: 2 + n = -13.114877049 Solving 2 + n = -13.114877049 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + n = -13.114877049 + -2 Combine like terms: 2 + -2 = 0 0 + n = -13.114877049 + -2 n = -13.114877049 + -2 Combine like terms: -13.114877049 + -2 = -15.114877049 n = -15.114877049 Simplifying n = -15.114877049Solution
The solution to the problem is based on the solutions from the subproblems. n = {11.114877049, -15.114877049}Solution
n = {11.114877049, -15.114877049}
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